This invention in general relates to displacement measurement interferometry and more particularly to apparatus by which the undesirable effects of ghost images on measurement signals can be substantially reduced.
Ghost images can be formed in displacement measurement interferometers through reflections from internal components in such a way that ghost beams overlap signal beams to cause significant errors. To be more concrete about the nature of ghost beams, reference is now made to FIG. 1 which shows an example of a high-stability plane mirror interferometer (HSPMI) that is a common type of displacement interferometer for stage metrology (For further examples see, e.g., Dr. C. Zanoni, Differential Interferometer Arrangements for Distance and Angle Measurements: Principles, Advantages and Applications, VDI BERICHTE NR. 749, 1989). It is evident from FIG. 1 that there are many opportunities for generating accidental reflections, resulting in "ghost" beams. Some of these reflections mix coherently in the interferometer to introduce nonlinearities. In particular, the front and back surfaces of measurement waveplate, W.sub.R shown in FIG. 1 generate ghost beams that can perfectly overlap the desired measurement beam. Unlike many of the reflections from the glass components, the polarization properties of the waveplate prevent separation of ghost beams by their polarization state. The resulting nonlinearity is potentially more serious than the commonly known error sources such as polarization mixing.
Most single-surface reflections may be defeated by tilting the various components of the interferometer with respect to each other and with respect to the stage mirror. These tilts diminish the effect of ghost beams by introducing tilt between them and the main beam. In other words, there are too many tilt fringes in these beams to generate strong interference signals. However, because there are 20 surface reflections for both the measurement and reference beams as shown in FIG. 1, there are 400 possible ghost beam paths involving two accidental reflections. As is the case with single-surface reflections, deliberately tilting the components removes many of the most troublesome two-surface reflections, provided that the two surfaces are not angled such as to cancel out the tilts. Unfortunately, many of the two-surface reflections involve the same optical component with a retroreflection in between. The two reflection angles cancel, resulting in a ghost beam that adds coherently to the main beams.
FIGS. 2 and 3 show two examples of ghost beam paths involving two surface reflections from the measurement waveplate. While the paths of these ghost beams are shown separated, it will be appreciated that, in reality, they overlap the principal interferometer beams. Because of the retroreflector, attempts to avoid these paths by tilting the waveplate fail, for the same reason that the interferometer accommodates tips and tilts in the stage mirror. No matter how the wave plate is tilted, ghost beams will find their way to the detector.
To be quatitative, the peak-valley (PV) error .delta.x in a plane-mirror interferometer resulting from a ghost beam of relative electric field amplitude .epsilon. is given by: ##EQU1## A quartz waveplate with a reflectivity of 0.5% nets a value .epsilon. of 0.005 after two reflections, and consequently .delta.x=0.25 nm for each of the contributions shown in FIGS. 2 and 3. In comparison, the contribution from HSPMI polarization mixing in a high-quality beam splitter (&lt;0.1% extinction) is an order of magnitude smaller (0.05 nm).
While there has been considerable attention on frequency and polarization mixing as error sources in these interferometers, there has been a noticeable absence of any treatment of problems attributed to ghost reflections. For example, in Appl. Opt. 37(28), 6696-6700 (1998), Wu and Deslattes briefly discuss the causes and effects of ghosts and note that some materials, such as mica and calcite, are poor substrates for AR coatings. However, they do not describe any means for reducing these ghosts.
Consequently, it is a primary object of the present invention to provide apparatus by which the effects of undesirable ghost beams generated in a displacement interferometer may be reduced.
Another principal object of the invention is to eliminate the possibility of coherent second-order ghost reflections from the measurement waveplate of a high stability plane mirror interferometer (HSPMI) as well as other plane-mirror interferometer types of architectures.
Other objects of the invention will in part be obvious and in part appear hereinafter when the following detailed description is read in connection with the drawings.